DUBAI/LONDON/CAIRO (Reuters) - Al Qaeda may have been pushed out of the enclave it carved out in Yemen as the country descended into civil war, but the militants are still entrenched in other parts of the country's south, reaping profits from smuggled fuel.

Scores of militants were killed in a Gulf Arab-backed offensive on Al Qaeda's de facto capital of Mukalla, Yemen's third largest seaport, but hundreds fled to neighboring Shabwa province and beyond.

Home to Yemen's largest industrial project, a now-shut liquefied natural gas export facility at Belhaf, Shabwa is divided among al Qaeda, government troops loyal to President Abd-Rabbu Mansour Hadi, Houthi forces and armed tribes.

Tribal sources say all sides are benefiting at a time of extreme fuel shortages around the country.

"There are five checkpoints in Shabwa between Bir Ali and Ataq leading to the (Houthi-controlled) interior ... one by the army, one by a tribal militia and one by the acting governor. Al Qaeda maintains two at Azzan," a local tribal leader said.

General Faraj al-Buhsani, commander of the Yemeni forces which routed AQAP in Mukalla, concurred.

"In Azzan (al Qaeda) has a hub for the trade in oil products coming from Belhaf and that area in the direction of Shabwa which is ongoing. We are hearing about this continuously."

Aid groups say Yemen in an average recent month brings in less than 10 percent of the more than 500,000 tonnes of fuel it needs, partly because many Yemeni ports are subject to a Gulf Arab quasi-blockade to prevent arms reaching the Houthis.

Director of the Shabwa governor's office, Muhsin al-Haj, defended the province's role in the illegal trade when it is struggling to maintain security with limited outside help.

"Shabwa is running on the most basic resources," he told Reuters. "In a province of 42,000 sq km, we have just two security cars, and they're not even armed."

A YEAR UNDER AQAP

Founded in the 1990s, AQAP's re-emergence is a striking unintended consequence of the Saudi-led intervention in Yemen in March 2015, prompted by gains made against the government by Houthi rebels allied to Saudi's arch-enemy, Iran.

Before the military's April 24-25 offensive, the group enjoyed relative prosperity along 600 km (373 miles) of Yemen's southern coastline, raking in around $2 million every day mostly by taxing goods entering Mukalla by ship, as documented in a Reuters investigation in early April. The group also extorted $1.4 million from the national oil company.

In its year of control, the militants gained the grudging acceptance of many locals in the long-marginalized south by putting its economic resources to work in development projects. Some residents told Reuters they preferred the stability of al Qaeda's rule to living in a war zone contested by armed groups.

For their part, the militants appeared to want to avoid dragging a potentially sympathetic civilian population into a conflict when the military attacked, and simply withdrew.

It was a change in tack for the group, which conducted a series of attacks in Yemen, including on the now-abandoned U.S. embassy in Sanaa, and claimed responsibility for the shootings at French satirical magazine Charlie Hebdo in January 2015.

Tribal sources say Al Qaeda militants have agreed not to obstruct the lucrative smuggling trade and instead inserted themselves into the illicit networks.

"Al Qaeda takes its share of oil smuggling at the ports in Shabwa through intermediaries and there is an agreement between them and the tribes that the one won't stand in the way of the other," one tribal source said.

SMALL CRAFT

Local officials and international shipping sources say the smuggling is conducted through small craft, including wooden dhows, alighting at fishing villages and hamlets.

One shipping source pointed to at least three small ships, which included tankers, that were involved in fuel smuggling activity around Bir Ali and surrounding areas since the government took over Mukalla.

"There are a number of small harbors around that area that have become possible conduits for illicit smuggling activity," said one shipping source. "It usually involves very small ships that can discharge their cargoes more easily given the smaller quantities involved.

"The vessels make deviations from their normal navigational courses and switch off their transponders close to the shorelines of these areas."

Two separate trade sources familiar with trading movements in Yemen also pointed to smuggling activity around those areas, involving ships carrying small loads of around 1,000 tonnes of fuel oil or diesel.

Yemeni military and coalition officials say that despite an apparent pause, they are continuing to fight to destroy AQAP.

"Al Qaeda is taking losses in Yemen and will continue to do so," Saudi Foreign Minister Adel al-Jubeir told a press conference in Berlin on Wednesday.

"There is no magic wand that one can wave that leads to the defeat of al Qaeda. It takes time ... we are determined to wage this battle until we defeat them."

Elisabeth Kendall, a Yemen scholar at Oxford University, said the group's new tactics could make it harder to root out, however.

"They're always going to keep melting away and now that they have a lot of money, they can buy their way into the population and reach places the government can't and gain traction."